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Answer:
[tex] \sf \frac{34}{31} - \frac{9}{45} = \frac{139}{155} [/tex]
Step-by-step explanation:
[tex] \sf \frac{34}{31} - \frac{9}{45} = \, ?[/tex]
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(34/31, 9/45) = 1395
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
[tex] \sf \left(\frac{34}{31} \times \frac{45}{45}\right) - \left(\frac{9}{45} \times \frac{31}{31}\right) = \, ?[/tex]
Complete the multiplication and the equation becomes
[tex] \sf \frac{1530}{1395} - \frac{279}{1395} = \, ?[/tex]
The two fractions now have like denominators so you can subtract the numerators.
Then:
[tex] \sf \frac{1530 - 279}{1395} = \frac{1251}{1395}[/tex]
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 1251 and 1395 using
GCF(1251,1395) = 9
[tex] \sf \frac{1251 \div 9}{1395 \div 9} = \frac{139}{155} [/tex]
Therefore:
[tex] \sf \frac{34}{31} - \frac{9}{45} = \frac{139}{155} [/tex]